According to what Danielle told the Losties at various points, she was seven months pregnant when she came to the island. Her scientific expedition picked up a radio signal which just had the numbers repeating over and over. They went to investigate and crashed on the island.
Then everyone in her group started getting sick from something, and she actually killed the last one herself (her lover Robert). Three days before she gave birth she found the radio tower and changed the message. 16 years later, here we are!
You might want to note that the times in her story would seem to contradict the times as given by Mr. Invincible, the Russian Mkhail, who claims to have arrived on the island in 1993 and was witness to "the purge" of the original Dharma people (unless Alex was taken by Dharma, and then "rescued" by Ben and the others?).